Related papers: Fusion rules and the Patera-Sharp generating-funct…
Tensor network methods are powerful and efficient tools to study the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods were applied to lattice gauge theories,…
Central pseudoscalar production in $pp$ scattering is suppressed at small values of $Q_\perp$, where $Q$ is defined as the difference between the momenta transferred from the two protons. Such a behaviour is expected if the production…
In this short note, I introduce to essential conceptual features and main building blocks of matrix element merging algorithms, operating on fixed order calculations both at leading order and next-to-leading order. The intention is purely…
In this article, we consider the weighted partition function $p_f(n)$ given by the generating series $\sum_{n=1}^{\infty} p_f(n)z^n = \prod_{n\in\mathbb{N}^{*}}(1-z^n)^{-f(n)}$, where we restrict the class of weight functions to strongly…
The powers of generating functions and its properties are analyzed. A new class of functions is introduced, based on the application of compositions of an integer $n$, called composita. The methods for obtaining reciprocal and reverse…
We solve general 1-matrix models without taking the double scaling limit. A method of computing generating functions is presented. We calculate the generating functions for a simple and double torus. Our method is also applicable to more…
Traditionally, different types of feature operators (e.g., convolution, self-attention and involution) utilize different approaches to extract and aggregate the features. Resemblance can be hardly discovered from their mathematical…
Establishing the fusion rules of anyonic quasiparticles in fractional quantum Hall fluids is essential for understanding their underlying topological order. Building on the conjecture that key topological properties are encoded in the "DNA"…
We develop the theory of weighted P-partitions, which generalises the theory of P-partitions from labelled posets to weighted labelled posets. We define the related generating functions in the natural way and compute their product,…
For loop integrals, the reduction is the standard method. Having an efficient way to find reduction coefficients is an important topic in scattering amplitudes. In this paper, we present the generation functions of reduction coefficients…
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include condensed matter systems with quenched disorder (e.g. spin glass) or cosmological systems in…
Properties of four quintic theta functions are developed in parallel with those of the classical Jacobi null theta functions. The quintic theta functions are shown to satisfy analogues of Jacobi's quartic theta function identity and…
We calculate the production of pairs of $\chi_c(J)$ mesons with all possible combinations of $J=0,1,2$. The leading order production mechanism is the crossed-channel gluon exchange in the gluon-gluon fusion reaction. The building blocks are…
We study compositions of a positive integer $n$ in which the occurrence of even parts larger than a fixed threshold $k$ is controlled. More precisely, for each composition $m=(m_1,\dots,m_r)$ we consider the number of even parts strictly…
In his important 1920 paper on partitions, MacMahon defined the partition generating functions \begin{align*} A_k(q)=\sum_{n=1}^{\infty}\mathfrak{m}(k;n)q^n&:=\sum_{0< s_1<s_2<\cdots<s_k}…
We give a Pieri-type formula for the sum of $K$-$k$-Schur functions $\sum_{\mu\le\lambda} g^{(k)}_{\mu}$ over a principal order ideal of the poset of $k$-bounded partitions under the strong Bruhat order, which sum we denote by…
We study the structure of fusion rules for the triplet $W$-algebra $\mathcal{W}_{p_+,p_-}$. By using the vertex tensor category theory developed by Huang, Lepowsky and Zhang, we rederive certain non-semisimple fusion rules given by…
Extending the method proposed in [arXiv:1109.5524], we derive QQ-relations (functional relations among Baxter Q-functions) and T-functions (eigenvalues of transfer matrices) for fusion vertex models associated with the twisted quantum…
We investigate one-particle semi-inclusive processes in lepton-hadron scattering. In unpolarized scattering order $Q^{-1}$ corrections appear only when transverse momenta are detected. We consider the twist two and three matrix elements and…
I review to which extent the properties of pseudoscalar mesons can be understood in terms of the underlying quark (and eventually gluon) structure. Special emphasis is put on the progress in our understanding of eta-eta' mixing.…